Mismatch of Displacement Input in Dynamic Analysis

FLAC2D
1

Hi Everyone and @itascan.

I am currently working on modeling a dynamic analysis of a tailings dam. I am performing some verifications to validate the model, and one of them is to verify if the input ground motion matches the calculated accelerations, velocities, and displacements. Here are some graphs of the input ground motion.

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Following this, I am presenting the numerical calculations of the accelerations, velocities, and displacements at the base of the model in the horizontal direction.

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Note that the accelerations and velocities are approximately in agreement with the input ground motion. However, the horizontal displacement does not match the input displacement. Does anyone have suggestions for resolving this issue?

Thank you.

2

General steps would be:

  1. Verify that your input ground motion been baseline corrected. If not the built-in Dynamic Input Wizard is quite good for that.

  2. Check if your dynamic boundary conditions are applied correctly? Ensure your model is in static equilibrium before assigning free-field and quiet boundaries. Try running the model with no input motion and see if it stays still.

  3. Ensure your grid size is appropriate. If needed, high frequencies in your input motion can filtered out, or your grid size needs to be adjusted to prevent accumulation of errors.

3

Hi, @paul.

I have checked all the points you mentioned, but I still haven’t been able to resolve the issue. There is a strange behavior at the base. The displacement graph I sent shows differential displacements at the base of the model. When I monitor the displacements in a vertical section of the 2D model, the displacements are approximately equal.

The wharf project example from FLAC2D shows the pattern I expected to observe in my model, as shown in the image below.

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I still haven’t figured out the reason for this behavior. Do you or @cheng have any further suggestions to check this behavior?

4

Hello @JonathasBB,
What kind of input motion are you using in your model? A stress-time history or a velocity-time history, or something different?

5

Hello @dblanksma,

I’m transforming the velocity-time history into a stress-time history and applying it to a compliant base.

6

Okay, in that case the input stress-time history will not be the same has the actual motion at the base since the base motion is a superposition of the input motion and reflected waves. Boundary reflection as well has different material stiffnesses will wave to reflect and influence the recorded motions at the base.

7

Right, I understand it.

I expect to have the result close to the input, as shown in the graph with the wharf project. In my analysis, the displacement-time history may be zero at the end of the time period because I have already performed a baseline correction.

What do you suggest I do?

8

Since the data file is not available, we can only make some guesses:

  1. If the base zones are not linear elastic, yielding might influence displacement.
  2. If the moduli of the base zones are stress-dependent, it may have an impact.
  3. Uneven or non-uniform reflection of seismic waves from the surface might cause different stresses in the base zones.

The best approach might be to send the complete data file to Itasca (flac3dsupport@itascacg.com) and ensure they can reproduce the issue.

9

Hi Jonathas,

Looking at your original question about the displacements at the base of the model increasing with time, I may suggest that what is happening here is the phenomenon of base rotation. This phenomenon also exists in the Wharf example provided in the manual. This is more of a numerical/model artifact, and if all other outputs are as expected, I believe you can trust your model and ignore the displacement increase with time. We are currently working on addressing it in FLAC2D 9 by implementing automatic base rotation correction. Users may expect this functionality in the next point release (9.4).

Here’s the explanation of the phenomenon (taken from old FLAC manual):

When a dynamic simulation is performed, rotation of the model base may occur if

  • the dynamic loading is applied at the base of the model;
  • the boundary condition at the base is a quiet boundary;
  • free-field boundaries are applied along the side boundaries.

Rotation will be more pronounced for models in which the model depth along the side boundaries varies significantly (for example, in slope or embankment simulations). Wave transmission through the model can produce a variation in the distribution in stresses that becomes locked-in if material failure occurs. Consequently, the reaction forces along the side boundaries, calculated when the free-field boundaries were assigned at the initial equilibrium state of the model, may no longer satisfy equilibrium for the redistributed stress state in the model. The base of the model can then start to rotate.

If your model satisfies the criteria outlined above, you are probably seeing base rotation. Currently, the only practical thing you can do is to increase the depth of the model to somewhat “damp” the rotation (but it will not be completely eliminated).

Note that base rotation is not related to baseline correction and it depends on where history is taken.

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